A code tracking loop starts its operation only after initial acquisition has been achieved.
In the code acquisition process, the normalized delay error between the input signal and
the locally generated replica code, δ = (τ −τˆ)/Tc is reduced to the range δ < 1 chip, whereTc is the chip duration. The objective of the code tracking loop is to further reduce this error down to zero and then to track any changes in code delay (i.e., τ). This loop structure is well-known as Delay Lock Loop or Delay Locked Loop (DLL) [29]. There are several delay tracking loop structures, DLL is only one of them and is the focus area of the thesis.
Figure 5.3: Simplified block diagram of a conventional non-coherent DLL [29]
A conceptual simplified block diagram of a conventional non-coherent DLL is shown in Figure 5.3. In a conventional non-coherent DLL as presented in Figure 5.3, the input signal is correlated with two locally generated, mutually delayed early and late replicas of the PRN code [29]. The spacing between early and late replicas is denoted as ∆. The DLL spacing (i.e., ∆) has significant impact on the performance of the discriminator-based DLL algorithms which is described in section 6.2. Referring to Figure 5.3, the results of the late correlator and the early correlator pass through a Band Pass Filter (BPF) and a square envelope detector. There difference produces an error signale(t). The error signal applies to a loop filter and the Numerically Controlled Oscillator (NCO) which drives the PRN sequence generator to correct timing. The discriminator function (i.e., D∆(δ)) in this example case can be represented as:
D∆(δ) =
whereR(δ) is the autocorrelation of the sequence. This is one of the most common struc-tures based on two correlators known as Early Minus Late (EML) correlator. There are different discriminator-based DLL algorithms which differ in terms of varying chip spacing
as well as varying the number of correlators used to form the discriminator function. The discriminator based algorithms are discussed in Chapter 6.
Several types of DLL have been proposed in the literature for code tracking. Mainly, there are two types of DLL: non-coherent and coherent [75, 76]. Non-coherent DLL uses nonlinear devices (such as squaring or absolute value) in order to remove the effect of data modulations and channel variations [75]. On the contrary, coherent DLL does not suffer from squaring losses and gain imbalances [77, 78]. However, non-coherent DLL is used in the thesis work as it is of interest in DS-CDMA systems where code acquisition and tracking must be performed prior to obtaining carrier synchronization.
The performance of a DLL is well-characterized by the so-called S-curve, which presents the expected value of the the error signal as a function of the reference parameter error (i.e., the code mismatch) [29, 31, 76]. The mathematical definition of the S-curve for DLL is given in equation 5.1. The intuition behind the S-curve is the fact that searching for maxima in the correlation function is equivalent with finding the zeros of the gradient, which can be approximated by first-order differences [75].
−2 −1.5 −1 −0.5 0 0.5 1 1.5 2
−0.5
−0.4
−0.3
−0.2
−0.1 0 0.1 0.2 0.3 0.4 0.5
S−curve
Delay Error [chips]
Non−coherent DLL
Figure 5.4: S-curve for non-coherent DLL in single path Rayleigh fading channel model Figure 5.4 represents one example S-curve for non-coherent DLL in single path Rayleigh fading channel model with average tap power 0 dB. In this example case, the delay of the LOS path can be estimated by finding the zero crossing from above to below. As it can be noticed from Figure 5.4 that there are some false lock points at about ±0.5 chips. This is due to fact that the ACF of SinBOC(1,1) modulated signal has side lobe peaks at±0.5 chips. This situation is even more challenging in the presence of randomly separated multipaths. This is still an open research issue to deal with the false lock points, especially in multipath fading channel models. However, as mentioned in [75], DLL-based
techniques have reduced ability to deal with closely spaced path scenarios under realistic assumptions (such as presence of errors in the channel estimation process) as well as have the possibility to lose the lock (i.e., start to estimate the delays with high estimation error) due to feed-back error propagation.
Code Tracking Algorithms
In general, the tracking algorithms can be grouped into two main categories: feed-back technique and feed-forward technique [75, 79]. Code tracking algorithms based on feed-back technique form a discriminator function at the receiver, find a delay estimate based on the discriminator, and feed it back in the loop so that it could be used in the following delay estimation. The most known feed-back structures are also known as DLLs [9, 80, 81, 82, 83]. The feed-back code tracking algorithms which are analyzed in the thesis are mentioned below:
• Wide Correlator
• Narrow Correlator
• High Resolution Correlator
• Multiple Gate Delay Correlator
On the contrary, feed-forward technique is based on a threshold computation which should be determined according to channel condition [75, 79]. In the thesis, the following feed-forward code tracking algorithms are analyzed:
• Multipath Estimating Delay Lock Loop
• Differential Order 2 Scheme
• Matched Filter
It is the general belief that feed-forward technique is more complex than the feed-back technique due to a higher number of correlators (usually needed) and to some additional processing that might be needed at the receiver. However, it is also possible to combine
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feed-back with feed-forward delay estimation so that the combined approach can utilize the advantages from both the techniques. One such algorithm is proposed herein which is the main focus area of the thesis. PT is the proposed novel algorithm which combines both feed-back and feed-forward techniques and utilizes the statistical properties of the correlation function in the process of delay estimation. This new algorithm is extensively compared with the existing feed-back and feed-forward algorithms mentioned earlier. The simulation results are presented in Chapter 8. All the above mentioned code tracking algorithms are discussed in what follows whereas the new PT algorithm is described in detail in the following chapter.
6.1 Wide Correlator
The classical tracking structure for spread spectrum systems is the wide correlator, where two correlators spaced at ∆W EM L= 1 chip from each other are used in the receiver to form a discriminator function, whose zero crossings determine the multipath delays [84, 85]. On the basis of autocorrelation function introduced in Figure 6.1, the corresponding EML code discriminator of SinBOC(1,1) modulated signal can be computed. The wide correlator or Wide EML (WEML) is computed by subtracting an early and a late version of the correlation function illustrated in Figure 6.1, using a chip spacing of 1 chip. We remark that a zero crossing from below corresponds here to the correct delay. Then a discriminator functionDW EM L is formed of the type:
DW EM L(τ) =
whereR(τ) is the ACF of the received signal and auto-generated replica code, and ∆W EM L
is the early-late chip spacing for wide EML.